Question

Construct a rhombus of side $6cm$ and one diagonal of length $10cm$. The length of the other diagonal is:

• A. $4.2cm$
• B. $6.6cm$
• C. $5.5cm$
• D. $7.4cm$

Answer 1

The correct option is B $6.6cm$

$\Rightarrow$ We know that all the sides of the rhombus are equal. We have given side is 6cm and one diagonal is 10cm.

$\Rightarrow$ Draw a line segment PQ = 6cm.

$\Rightarrow$ Take P as a center with radius 10cm and draw an arc.

$\Rightarrow$ Take Q as a center with radius 6cm and draw an arc meeting previous arc at point R.

$\Rightarrow$ Take P as a center with radius 6cm and draw an arc.

$\Rightarrow$ Take R as a center with radius 6cm and draw an arc meeting previous arc at point S.

$\Rightarrow$ Join PR, QR, RS, PS and QS.

$\Rightarrow$ Thus, PQRS is the required rhombus.

$\Rightarrow$ We have to measure length of the other diagonal which is QS.

$\therefore$ $QS=6.6cm$